Titlebook: Lectures on Choquet‘s Theorem; Robert R. Phelps Book 2001Latest edition Springer-Verlag Berlin Heidelberg 2001 Choquet‘s Theorem.Compact c

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https://doi.org/10.1007/b76887Choquet‘s Theorem; Compact convex sets; DEX; approximation theory; average; eXist; ergodic theory; form; fun

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Applications of the Choquet boundary to resolvents,Let . be a compact Hausdorff space, and suppose that for each λ > 0 there is a linear transformation . . : .(X) → .(X) such that . . ≧ 0 (i.e., . . . ≧ 0 whenever . ≧ 0) and . .1 = 1/λ. We call the family of operators . .(λ > 0) a . if the following identity is valid for all λ, λ′ > 0: . . - . . = (λ - λ′). . . ..

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Application to invariant and ergodic measures,Let . be a set, . a σ-ring of subsets of ., and . a family of measurable functions from . into ., i.e., for each . in . we have . : . ’ . and . . . ∈ . whenever . ∈ . A nonnegative finite measure μ on . is said to be . (or .-invariant) if μ(. . .)= μ(.) for each . in . and . in ..